Structure of background noise for a 5 × 5 bin field at different thresholds ρ resulting in different probabilities for a black pixel. Probability distributions of a) area A; b) perimeter P; c) Euler characteristic χ. d) Compatibility of Euler characteristic χ, with the sum of all probabilities , which is visualized by the equally large colored regions beneath the graphs in c) and d) – mind the different scales.